Thomas Whitcombe was a well known maritime artist of the late 18th and early 19th century. He was born in London. Among his over 150 pictures of the Royal Navy in action or otherwise are several that depict Gibraltar. The following are the few that I have been able to trace.

One of a collection of fifty plates produced for a book called The Naval Achievements of Great Britain published after the end of the Napoleonic Wars - it is my header picture

A Royal Navy Third Rate heeling in the breeze as she arrives off Gibraltar to join a Squadron of the Red lying at anchor inshore

British Man of War before Gibraltar

Comparison of the ships depicted in the above two paintings.
Whatever the difference between a 'Man of War' and a 'Third Rate' - I am certain it didn't just involve adding or removing a few cannon from the second deck

The Destruction of the Floating Batteries at Gibraltar in 1782
This may be the artist's first exhibit at the Royal Academy in 1783.